File: i1.c

package info (click to toggle)
python-scipy 0.18.1-2
  • links: PTS, VCS
  • area: main
  • in suites: stretch
  • size: 75,464 kB
  • ctags: 79,406
  • sloc: python: 143,495; cpp: 89,357; fortran: 81,650; ansic: 79,778; makefile: 364; sh: 265
file content (186 lines) | stat: -rw-r--r-- 4,044 bytes parent folder | download | duplicates (4)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
/*                                                     i1.c
 *
 *     Modified Bessel function of order one
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, i1();
 *
 * y = i1( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns modified Bessel function of order one of the
 * argument.
 *
 * The function is defined as i1(x) = -i j1( ix ).
 *
 * The range is partitioned into the two intervals [0,8] and
 * (8, infinity).  Chebyshev polynomial expansions are employed
 * in each interval.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0, 30       30000       1.9e-15     2.1e-16
 *
 *
 */
/*							i1e.c
 *
 *	Modified Bessel function of order one,
 *	exponentially scaled
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, i1e();
 *
 * y = i1e( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns exponentially scaled modified Bessel function
 * of order one of the argument.
 *
 * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0, 30       30000       2.0e-15     2.0e-16
 * See i1().
 *
 */

/*                                                     i1.c 2          */


/*
 * Cephes Math Library Release 2.8:  June, 2000
 * Copyright 1985, 1987, 2000 by Stephen L. Moshier
 */

#include "mconf.h"

/* Chebyshev coefficients for exp(-x) I1(x) / x
 * in the interval [0,8].
 *
 * lim(x->0){ exp(-x) I1(x) / x } = 1/2.
 */

static double A[] = {
    2.77791411276104639959E-18,
    -2.11142121435816608115E-17,
    1.55363195773620046921E-16,
    -1.10559694773538630805E-15,
    7.60068429473540693410E-15,
    -5.04218550472791168711E-14,
    3.22379336594557470981E-13,
    -1.98397439776494371520E-12,
    1.17361862988909016308E-11,
    -6.66348972350202774223E-11,
    3.62559028155211703701E-10,
    -1.88724975172282928790E-9,
    9.38153738649577178388E-9,
    -4.44505912879632808065E-8,
    2.00329475355213526229E-7,
    -8.56872026469545474066E-7,
    3.47025130813767847674E-6,
    -1.32731636560394358279E-5,
    4.78156510755005422638E-5,
    -1.61760815825896745588E-4,
    5.12285956168575772895E-4,
    -1.51357245063125314899E-3,
    4.15642294431288815669E-3,
    -1.05640848946261981558E-2,
    2.47264490306265168283E-2,
    -5.29459812080949914269E-2,
    1.02643658689847095384E-1,
    -1.76416518357834055153E-1,
    2.52587186443633654823E-1
};

/* Chebyshev coefficients for exp(-x) sqrt(x) I1(x)
 * in the inverted interval [8,infinity].
 *
 * lim(x->inf){ exp(-x) sqrt(x) I1(x) } = 1/sqrt(2pi).
 */
static double B[] = {
    7.51729631084210481353E-18,
    4.41434832307170791151E-18,
    -4.65030536848935832153E-17,
    -3.20952592199342395980E-17,
    2.96262899764595013876E-16,
    3.30820231092092828324E-16,
    -1.88035477551078244854E-15,
    -3.81440307243700780478E-15,
    1.04202769841288027642E-14,
    4.27244001671195135429E-14,
    -2.10154184277266431302E-14,
    -4.08355111109219731823E-13,
    -7.19855177624590851209E-13,
    2.03562854414708950722E-12,
    1.41258074366137813316E-11,
    3.25260358301548823856E-11,
    -1.89749581235054123450E-11,
    -5.58974346219658380687E-10,
    -3.83538038596423702205E-9,
    -2.63146884688951950684E-8,
    -2.51223623787020892529E-7,
    -3.88256480887769039346E-6,
    -1.10588938762623716291E-4,
    -9.76109749136146840777E-3,
    7.78576235018280120474E-1
};

double i1(x)
double x;
{
    double y, z;

    z = fabs(x);
    if (z <= 8.0) {
	y = (z / 2.0) - 2.0;
	z = chbevl(y, A, 29) * z * exp(z);
    }
    else {
	z = exp(z) * chbevl(32.0 / z - 2.0, B, 25) / sqrt(z);
    }
    if (x < 0.0)
	z = -z;
    return (z);
}

/*                                                     i1e()   */

double i1e(x)
double x;
{
    double y, z;

    z = fabs(x);
    if (z <= 8.0) {
	y = (z / 2.0) - 2.0;
	z = chbevl(y, A, 29) * z;
    }
    else {
	z = chbevl(32.0 / z - 2.0, B, 25) / sqrt(z);
    }
    if (x < 0.0)
	z = -z;
    return (z);
}